$$ \begin{aligned} 1\,\text{u}&=\frac{1}{12}\times\text{ mass of }\;^{12}_{\;\,6}C {\color{gray}\quad\text{ Unified Atomic mass unit}}\\ &=1.6605\times10^{-27}\,\text{kg}\leftarrow\left\{\begin{aligned} &m_p=1.673\times10^{-27}\,\text{kg} \\ &m_n=1.675\times10^{-27}\,\text{kg} \end{aligned}\right. \end{aligned} $$

<aside> <img src="https://s3-us-west-2.amazonaws.com/secure.notion-static.com/c9bfc53d-fc55-4435-bb19-8c530a2a9da6/Standard_atomic_wieght.png" alt="https://s3-us-west-2.amazonaws.com/secure.notion-static.com/c9bfc53d-fc55-4435-bb19-8c530a2a9da6/Standard_atomic_wieght.png" width="40px" /> Standard atomic weight:

$$ \text{Standard atomic weight(u)}=\sum_i\text{natural abundance}_i\times\text{weight}_i $$

Example: Calculate the standard atomic weight of carbon given that its natural abundance is $98.9\%\, ^{12}C$ and $1.1\%\, ^{13}C$

$$ \text{Stand. Atom. W.}=0.989\times 12+0.011\times13.003=12.01 \,\text{u} $$

</aside>

<aside> <img src="https://s3-us-west-2.amazonaws.com/secure.notion-static.com/266f0708-463c-4df9-88a4-19e30ed8070a/Binding_energy.png" alt="https://s3-us-west-2.amazonaws.com/secure.notion-static.com/266f0708-463c-4df9-88a4-19e30ed8070a/Binding_energy.png" width="40px" /> Binding energy:

$$ E=\Delta mc^2 $$

</aside>

<aside> <img src="https://s3-us-west-2.amazonaws.com/secure.notion-static.com/186a7516-6acc-4c31-89a6-03e645a1b16b/Ionizing.png" alt="https://s3-us-west-2.amazonaws.com/secure.notion-static.com/186a7516-6acc-4c31-89a6-03e645a1b16b/Ionizing.png" width="40px" /> Ionizing: pulling an electron off its “orbit

$$ V\simeq\frac{e^2}{4\pi\varepsilon_0\times 1 \mathring{A}} $$

</aside>

<aside> <img src="https://s3-us-west-2.amazonaws.com/secure.notion-static.com/36453f93-7ebd-4ca9-bf17-2cc853b740d4/moles_and_more.png" alt="https://s3-us-west-2.amazonaws.com/secure.notion-static.com/36453f93-7ebd-4ca9-bf17-2cc853b740d4/moles_and_more.png" width="40px" /> Moles and more:

$$ \begin{aligned} M&=\text{molar mass in g/mol} \\ m&=\text{mass in g}\\ n&=\text{number of moles} \end{aligned} $$

$$ M=\frac{m}{n} $$

$$ 1 \text{ mol has }6.022\times10^{23} \,\text{atoms, aka Avogadro's Number} $$

$$ \text{density: } \rho=\frac{m}{V} $$

</aside>